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Question Number 147892 Answers: 1 Comments: 0

if x;y;z>1 then: (√((((x−1)(y−1)(z−1))/((x+1)(y+1)(z+1))) )) < ((xyz)/8)

$${if}\:\:\:{x};{y};{z}>\mathrm{1}\:\:\:{then}: \\ $$$$\sqrt{\frac{\left({x}−\mathrm{1}\right)\left({y}−\mathrm{1}\right)\left({z}−\mathrm{1}\right)}{\left({x}+\mathrm{1}\right)\left({y}+\mathrm{1}\right)\left({z}+\mathrm{1}\right)}\:}\:<\:\frac{{xyz}}{\mathrm{8}} \\ $$

Question Number 147884 Answers: 0 Comments: 0

∫_0 ^1 e^(−x) x^a dx a>0

$$\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{−{x}} {x}^{{a}} {dx}\:\:{a}>\mathrm{0} \\ $$$$ \\ $$

Question Number 147882 Answers: 2 Comments: 0

if ((6(√3) + 10))^(1/3) − ((6(√3) − 10))^(1/3) = x find (x^3 /(10−3x)) = ?

$${if}\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{6}\sqrt{\mathrm{3}}\:+\:\mathrm{10}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{6}\sqrt{\mathrm{3}}\:−\:\mathrm{10}}\:=\:\boldsymbol{{x}} \\ $$$${find}\:\:\:\frac{{x}^{\mathrm{3}} }{\mathrm{10}−\mathrm{3}{x}}\:=\:? \\ $$

Question Number 147879 Answers: 1 Comments: 0

Question Number 147878 Answers: 1 Comments: 0

Find the sum to n term: 1.2.3 + 4.5.6 + 7.8.9 + ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\:\mathrm{n}\:\:\mathrm{term}:\:\:\:\:\:\mathrm{1}.\mathrm{2}.\mathrm{3}\:\:+\:\:\mathrm{4}.\mathrm{5}.\mathrm{6}\:\:+\:\:\mathrm{7}.\mathrm{8}.\mathrm{9}\:\:+\:\:... \\ $$

Question Number 147873 Answers: 1 Comments: 0

Question Number 147877 Answers: 1 Comments: 2

Find the sum to close form. (1/(1.2.3)) + (1/(4.5.6)) + (1/(7.8.9)) + ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{close}\:\mathrm{form}. \\ $$$$\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{5}.\mathrm{6}}\:\:\:+\:\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{8}.\mathrm{9}}\:\:\:+\:\:\:...\:\:\: \\ $$

Question Number 147867 Answers: 3 Comments: 0

∫secx dx=?

$$\int\mathrm{sec}{x}\:{dx}=? \\ $$

Question Number 147863 Answers: 1 Comments: 0

calculate Σ_(n=0) ^∞ ((n!^2 )/((2n)!))

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{n}!^{\mathrm{2}} }{\left(\mathrm{2n}\right)!} \\ $$$$ \\ $$

Question Number 147862 Answers: 1 Comments: 0

calculate Σ_(n=0) ^∞ (n^2 /3^n )

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{n}^{\mathrm{2}} }{\mathrm{3}^{\mathrm{n}} } \\ $$

Question Number 147861 Answers: 0 Comments: 0

resoudre dans Z^2 x^2 −y^2 =3x

$$\mathrm{resoudre}\:\mathrm{dans}\:\mathrm{Z}^{\mathrm{2}} \:\:\:\:\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \:=\mathrm{3x} \\ $$

Question Number 147876 Answers: 1 Comments: 0

Question Number 147842 Answers: 0 Comments: 2

x ; y ; z > 0 { ((x+y^2 +z^3 = 3)),((y+z^2 +x^3 = 3)),((z+x^2 +y^3 = 3)) :} ⇒ x ; y ; z = ?

$${x}\:;\:{y}\:;\:{z}\:>\:\mathrm{0} \\ $$$$\begin{cases}{{x}+{y}^{\mathrm{2}} +{z}^{\mathrm{3}} \:=\:\mathrm{3}}\\{{y}+{z}^{\mathrm{2}} +{x}^{\mathrm{3}} \:=\:\mathrm{3}}\\{{z}+{x}^{\mathrm{2}} +{y}^{\mathrm{3}} \:=\:\mathrm{3}}\end{cases}\:\:\Rightarrow\:\:{x}\:;\:{y}\:;\:{z}\:=\:? \\ $$

Question Number 147837 Answers: 1 Comments: 0

Evaluate ∫((sin^8 θ−cos^8 θ)/(1−2sin^2 θcos^2 θ)) dθ

$${Evaluate} \\ $$$$\int\frac{\mathrm{sin}\:^{\mathrm{8}} \theta−\mathrm{cos}\:^{\mathrm{8}} \theta}{\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \theta\mathrm{cos}\:^{\mathrm{2}} \theta}\:{d}\theta \\ $$$$ \\ $$

Question Number 147835 Answers: 0 Comments: 0

prove that ∫cos 2θlog(((cos θ+sin θ)/(cos θ−sin θ)))=(1/2)sin 2θlog[tan ((π/4)+θ)+(1/2)log (cos 2θ)

$${prove}\:{that}\: \\ $$$$\:\:\int\mathrm{cos}\:\mathrm{2}\theta{log}\left(\frac{\mathrm{cos}\:\theta+\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta−\mathrm{sin}\:\theta}\right)=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}\theta{log}\left[\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}+\theta\right)+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}\:\left(\mathrm{cos}\:\mathrm{2}\theta\right)\right. \\ $$$$ \\ $$

Question Number 147828 Answers: 1 Comments: 0

Σ_(p=0) ^n psh(a+bp)

$$\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{psh}\left(\mathrm{a}+\mathrm{bp}\right) \\ $$

Question Number 147820 Answers: 1 Comments: 0

Σ_(p=0) ^n sh^2 (a+pb)

$$\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{sh}^{\mathrm{2}} \left(\mathrm{a}+\mathrm{pb}\right) \\ $$

Question Number 147819 Answers: 1 Comments: 0

Σ_(p=0) ^n ch^2 (a+pb)

$$\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{ch}^{\mathrm{2}} \left(\mathrm{a}+\mathrm{pb}\right) \\ $$

Question Number 147811 Answers: 1 Comments: 0

Question Number 147810 Answers: 1 Comments: 0

cos(x) ∙ cos(3x)=cos(5x) ∙ cos(7x) x = ?

$$\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\:\centerdot\:\boldsymbol{{cos}}\left(\mathrm{3}\boldsymbol{{x}}\right)=\boldsymbol{{cos}}\left(\mathrm{5}\boldsymbol{{x}}\right)\:\centerdot\:\boldsymbol{{cos}}\left(\mathrm{7}\boldsymbol{{x}}\right) \\ $$$$\boldsymbol{{x}}\:=\:? \\ $$

Question Number 147803 Answers: 0 Comments: 7

∫(((√(2−x^2 ))+(√(2+x^2 )))/( (√(4−x^4 ))))dx

$$\int\frac{\sqrt{\mathrm{2}−{x}^{\mathrm{2}} }+\sqrt{\mathrm{2}+{x}^{\mathrm{2}} }}{\:\sqrt{\mathrm{4}−{x}^{\mathrm{4}} }}{dx} \\ $$

Question Number 147800 Answers: 1 Comments: 0

Question Number 147799 Answers: 1 Comments: 0

∫(((√(2−x^2 ))+(√(2+x^2 )))/( (√(4−x^2 ))))dx

$$\int\frac{\sqrt{\mathrm{2}−{x}^{\mathrm{2}} }+\sqrt{\mathrm{2}+{x}^{\mathrm{2}} }}{\:\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 147795 Answers: 1 Comments: 2

Question Number 147791 Answers: 2 Comments: 3

If a + b + c + d = 1 a^2 + b^2 + c^2 + d^2 = 2 a^3 + b^3 + c^3 + d^3 = 3 a^4 + b^4 + c^4 + d^4 = 4 Evaluate: a^6 + b^6 + c^6 + d^6

$$\mathrm{If}\:\:\:\:\:\:\:\mathrm{a}\:\:+\:\:\mathrm{b}\:\:+\:\:\mathrm{c}\:\:+\:\:\mathrm{d}\:\:\:=\:\:\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\:\mathrm{b}^{\mathrm{2}} \:\:+\:\:\mathrm{c}^{\mathrm{2}} \:\:+\:\:\mathrm{d}^{\mathrm{2}} \:\:=\:\:\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{3}} \:\:+\:\:\mathrm{b}^{\mathrm{3}} \:\:+\:\:\mathrm{c}^{\mathrm{3}} \:\:+\:\:\mathrm{d}^{\mathrm{3}} \:\:=\:\:\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{4}} \:\:+\:\:\mathrm{b}^{\mathrm{4}} \:\:+\:\:\mathrm{c}^{\mathrm{4}} \:\:+\:\:\mathrm{d}^{\mathrm{4}} \:\:=\:\:\mathrm{4} \\ $$$$\mathrm{Evaluate}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{6}} \:\:+\:\:\mathrm{b}^{\mathrm{6}} \:\:+\:\:\mathrm{c}^{\mathrm{6}} \:\:+\:\:\mathrm{d}^{\mathrm{6}} \\ $$

Question Number 147788 Answers: 0 Comments: 0

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